A new fully adaptive multiresolution method is appliedfor the simulation of the complex dynamics of waves inexcitable media in electrocardiology, where the membranekinetics are given by the Alievâeuro"Panfilov or Luoâeuro"Rudy IImodels. Numerical experiments show that the automaticadaptation strategy tracks the spatio-temporal patternaccurately at a substantially reduced computational costif compared with fine-grid simulations. The nonlineardynamics of complex multiscale patterns can thus becomputed efficiently, also in the chaotic and turbulentregime which are currently beyond the frontiers ofmethods using regular discretizations.